How can you use the context package in Go to manage cancellation and timeouts in a concurrent environment?

In Go, the `context` package provides a powerful mechanism for managing cancellation and timeouts in a concurrent environment. It allows you to propagate signals and deadlines across goroutines and provides a way to gracefully cancel or timeout operations when needed.

The `context` package introduces the `Context` type, which represents the context of an operation. A `Context` can be created using the `context.Background()` function, which returns a background context that serves as the root of the context tree. You can then create derived contexts using the `context.WithCancel()` or `context.WithTimeout()` functions.

1. Cancellation:
To manage cancellation, you can create a context with cancellation capability using the `context.WithCancel()` function. This function returns a new derived context and a corresponding `cancel` function. When the `cancel` function is called, it signals that the operation associated with the context should be canceled.

Here's an example that demonstrates cancellation using the `context` package:

```
go`package main

import (
"context"
"fmt"
"time"
)

func main() {
// Create a context with cancellation capability
ctx, cancel := context.WithCancel(context.Background())

// Start a goroutine with the created context
go doWork(ctx)

// Simulate cancellation after some time
time.Sleep(2 * time.Second)
cancel()

// Wait for the goroutine to complete
time.Sleep(1 * time.Second)
}

func doWork(ctx context.Context) {
for {
select {
case <-ctx.Done():
fmt.Println("Operation canceled")
return
default:
// Perform some work
fmt.Println("Working...")
time.Sleep(500 * time.Millisecond)
}
}
}`
```
In the above example, the `doWork` function is executed in a separate goroutine and continuously performs some work. The `select` statement is used to check the cancellation signal from the context's `Done()` channel. When the `cancel` function is called in the main goroutine, the `Done()` channel receives a signal, and the `doWork` goroutine is gracefully canceled.
2. Timeouts:
The `context` package also provides a way to enforce timeouts for operations using the `context.WithTimeout()` function. This function creates a derived context that is automatically canceled after a specified duration.

Here's an example that demonstrates timeout using the `context` package:

```
go`package main

import (
"context"
"fmt"
"time"
)

func main() {
// Create a context with a timeout of 1 second
ctx, cancel := context.WithTimeout(context.Background(), 1*time.Second)
defer cancel()

// Start a goroutine with the created context
go doWork(ctx)

// Wait for the goroutine to complete
time.Sleep(2 * time.Second)
}

func doWork(ctx context.Context) {
for {
select {
case <-ctx.Done():
fmt.Println("Operation timed out")
return
default:
// Perform some work
fmt.Println("Working...")
time.Sleep(500 * time.Millisecond)
}
}
}`
```
In this example, the `doWork` function is again executed in a separate goroutine. However, this time, a timeout of 1 second is set using the `WithTimeout()` function. After 1 second, the context's `Done()` channel receives a signal, and the `doWork` goroutine is canceled due to the timeout.

Using the `context` package, you can effectively manage