
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 $n \geq 3$.

Suppose Fibonacci numbers $F_a$, $F_b$, $F_d$ form an increasing geometric sequence instead of arithmetic, and have $a + b + d = 3000$. Find the value of $a$ if $b-a = c = 2$ and $d = b+c$.

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