
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 \( P(x) = 1 + 8x + 4x^2 + 8x^3 + 4x^4 + \cdots \) for values of \( x \) for which this sum has finite value. Find \( P\left(\frac{1}{7}\right) \).

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