
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
The Fibonacci sequence is defined as $F_1 = F_2 = 1$ and $F_n = F_{n - 1} + F_{n - 2}$ for all $n \geq 3$.
If the Fibonacci numbers $F_a, F_b, F_c$ form a geometric sequence with $F_a$ being the smallest, and additionally, if $a + b + c = 1500$, compute $a$.

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