
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 \( F_{n} \) be the Fibonacci sequence, that is, \( F_{0}=0 \), \( F_{1}=1 \), and \( F_{n+2}=F_{n+1}+F_{n} \). Compute \( \sum_{n=0}^{\infty} \frac{F_{n}}{10^{n}} \).

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