
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
Given the circle $(x+2)^2+(y-2)^2=a$ intersects with the line $x+y+2=0$, and the length of the chord formed is $6$, determine the value of the real number $a$.

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