
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
Let \( x < 0.1 \) be a positive real number. Consider the series \( 4 + 4x + 4x^2 + 4x^3 + \ldots \), and the series \( 4 + 44x + 444x^2 + 4444x^3 + \ldots \). Suppose that the sum of the second series is four times the sum of the first series. Compute \( x \).

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