
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
Compute the value of $x$ such that:

$$\left(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \cdots\right)\left(1 - \frac{1}{3} + \frac{1}{9} - \frac{1}{27} + \cdots\right) = 1 + \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + \cdots.$$

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