
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 a sequence $\{a_n\}$ ($n\in\mathbb{N}^*$) with the first term being 2 and the common ratio being 3, calculate the value of $a_1C_{6}^{0} - a_2C_{6}^{1} + a_3C_{6}^{2} - a_4C_{6}^{3} + a_5C_{6}^{4} - a_6C_{6}^{5} + a_7C_{6}^{6}$.

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