
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
A dog's leash is \(4 \mathrm{~m}\) long and is attached to the corner of a \(2 \mathrm{~m} \times 2 \mathrm{~m}\) square doghouse at \(C\). The dog is attached to the other end of the leash, at \(D\). Find the area outside of the doghouse in which the dog can play.

Present the answer in LaTex format: \boxed{Your answer}
user