
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 expression
$$
\left(\left(\cdots\left(\left((x-2)^{2}-2\right)^{2}-2\right)^{2}-\cdots-2\right)^{2}-2\right)^{2},
$$
which contains $k$ nested sets of parentheses, remove the parentheses and combine like terms to obtain a polynomial. Find the coefficient of $x^{2}$ in this polynomial.

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