
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
Determine the coefficient of \( x^{2} \) after expanding and combining like terms in the expression

$$
\underbrace{\left(\ldots\left(\left((x-2)^{2}-2\right)^{n}-2\right)^{2}-\ldots-2\right)^{2}}_{k \text { times }}
$$

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