
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
Calculate the double integral \(\iint_{\Omega} \sqrt{\left|x^{2}-y^{2}\right|} \, dx \, dy\), where \(\Omega=\{(x, y): |x| + |y| \leq a\}\).

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