
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
In the sequence ${\{a_n\}}$, the equation $(a_1 + 2a_2 + 2^2a_3 + \cdots + 2^{n-1}a_n = (n \cdot 2^n - 2^n + 1)t)$ holds for any $n \in \mathbb{N}^*$, where $t > 0$ is a constant. If the solution set of the inequality $\frac{1}{a_2} + \frac{1}{a_4} + \frac{1}{a_8} + \cdots + \frac{1}{a_{2^n}} > \frac{m}{a_1}$ is ${n|n \geqslant 4, n \in \mathbb{N}^*}$, then the range of the real number $m$ is.

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