
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 the identity: $(x^2-x+1)^6 = a + a_1x + a_2x^2 + a_3x^3 + \ldots + a_{10}x^{10} + a_{11}x^{11} + a_{12}x^{12}$, then the value of $(a + a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12})^2 - (a_1 + a_3 + a_5 + a_7 + a_9 + a_{11})^2$ is __.

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