
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
For which smallest value of the parameter \( a \) will the coefficient of \( x^{4} \) in the expansion of the polynomial \( \left(1-2 x+a x^{2}\right)^{8} \) be equal to \(-1540\)?

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