
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
If $(x^2-3x+2)^5=a+a_1x+a_2x^2+\ldots+a_{10}x^{10}$,  
(1) Find $a_2$.  
(2) Find $a_1+a_2+\ldots+a_{10}$.  
(3) Find $(a+a_2+a_4+\ldots+a_8+a_{10})^2-(a_1+a_3+\ldots+a_7+a_9)^2$.

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