
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 $(X-2)^8 = a + a_1(x-1) + \ldots + a_8(x-1)^8$, then the value of $\left(a_2 + a_4 + \ldots + a_8\right)^2 - \left(a_1 + a_3 + \ldots + a_7\right)^2$ is (Answer in digits).

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