
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 $\{a_n\}$ that satisfies $(a_1 + 4a_2 + 4^2a_3 + \cdots + 4^{n-1}a_n = \frac{n}{4})$ $(n\in \mathbb{N}^*)$.

(I) Find the general formula for the sequence $\{a_n\}$;

(II) Let $(b_n = 2^n\log_4 a_n)$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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