
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 \( f(x) = a x + b \) where \( a \) and \( b \) are integers. If \( f(f(0)) = 0 \) and \( f(f(f(4))) = 9 \), find the value of \( f(f(f(f(1)))) + f(f(f(f(2)))) + \cdots + f(f(f(f(2014)))) \).

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