
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 (3x-1)^n = a_0 + a_1x + a_2x^2 + ... + a_nx^n, where the binomial coefficients are maximized for the fourth and fifth terms, find:
(1) $$\sum\limits_{i=1}^{n}$$|a_i|;
(2) $$\sum\limits_{i=1}^{n}$$|ia_i|;
(3) The term in the expansion with the largest absolute coefficient value.

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