
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 that $(2x - 1)^{7} = a_{7}x^{7} + a_{6}x^{6} + ... + a_{1}x + a_{0}$, find:
(1) $a_{0}$; (2) $a_{1} + a_{2} + ... + a_{7}$; (3) $a_{1} + a_{3} + a_{5} + a_{7}$.

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