
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, defined as $F_0 = 0$, $F_1 = 1$, and for $n \geq 0$, $F_{n+2} = F_{n+1} + F_n$. Compute the sum \[ \sum_{n=0}^\infty \frac{F_{2n+1}}{5^n}. \]

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