
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 \( f(1)=3 \), \( f(2)=5 \), and \( f(n+2)=f(n+1)+f(n) \) for positive integers \( n \). If \( c \) is the remainder of \( f(b) \) divided by 3, find the value of \( c \).

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