
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 that the sum of the coefficients of the expanded form of $(3x^2+ \sqrt{x})^n$ is $M$, the sum of the coefficients of the expanded form of $(3x^2- \sqrt{x})^{n+5}$ is $N$, and the sum of the coefficients of the expanded form of $(x+1)_n$ is $P$. If $M+N-P=2016$, find:
1. The term with the maximum binomial coefficient in the expanded form of $(2x^2- \frac{1}{x^2})^{2n}$.
2. The term with the maximum absolute value of the coefficient in the expanded form of $(2x^2- \frac{1}{x^2})^{2n}$.

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