
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 by $F_1 = 1, F_2 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for all $n \geq 3$. The Fibonacci numbers $F_a, F_b, F_c$ form an increasing arithmetic sequence. Suppose $a + b + c = 2253$, and the indices $a, b, c$ fit the pattern $b - 3, b, b + 3$. Determine the value of $b$.

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