
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 $\left(x+2\right)\left(2x-1\right)^{5}=a_{0}+a_{1}x+\ldots +a_{6}x^{6}$, then $a_{1}-a_{2}+a_{3}-a_{4}+a_{5}-a_{6}=$______,$a_{2}=\_\_\_\_\_\_$.

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