
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
Let \( p_{k}(x) = \underbrace{\left(\cdots\left(\left((x-2)^{2}-2\right)^{2}-2\right)^{2}-\cdots-2\right)^{2}}_{k \uparrow} \), where \( k \) is any given natural number. Determine the coefficient of the \( x^{2} \) term in \( p_{k}(x) \) with \( k \) layers of parentheses.

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