
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 $a_1(x+m)^4+a_2(x+m)^3+a_3(x+m)^2+a_4(x+m)+a_5=x^4$, let $m= \int_{0}^{\pi} (\sin x - 1 + 2\cos^2 \frac{x}{2})dx$, then $a_2=$ \_\_\_\_\_\_.

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