
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 $f_1(x) = \cos x$, and define $f_{n+1}(x)$ as the derivative of $f_n(x)$, that is, $f_{n+1}(x) = f'_n(x)$, where $n \in \mathbb{N}^*$. If the internal angle $A$ of $\triangle ABC$ satisfies $f_1(A) + f_2(A) + \ldots + f_{2013}(A) = 0$, then the value of $\sin A$ is.

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