
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 $(3x-1)^7 = a_7x^7 + a_6x^6 + \ldots + a_1x + a_0$, find  
(1) $a_1 + a_2 + \ldots + a_7$;  
(2) $a_1 + a_3 + a_5 + a_7$;  
(3) $a_0 + a_2 + a_4 + a_6$;  
(4) $|a_0| + |a_1| + |a_2| + \ldots + |a_7|$. (Calculate the final result)

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