
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 \((1-2x)^7 = \sum_{k=0}^{7} a_k x^k\), what is \(2a_2 + 3a_3 + 4a_4 + 5a_5 + 6a_6 + 7a_7\)?

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