
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 positive integer $m \in \mathbb{N}^*$, let $x$ be a positive number defined as $x = \frac{a_1}{2} + \frac{a_2}{2^2} + \dots + \frac{a_m}{2^m}$, where $|a_i| = 1$ for $1 \leq i \leq m$, $i \in \mathbb{N}^*$. Let $X_m$ denote the sum of all such numbers $x$.

1. Find $X_3$ and $X_4$.
2. Find $X_m$.

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