
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 the function $f_{0}(x) = \sin x - \cos x$, $f_{1}(x) = f'_{0}(x)$, $f_{2}(x) = f'_{1}(x)$, ..., $f_{n+1}(x) = f'_{n}(x)$, where $n \in \mathbb{N}$. Find the value of $f_{2013}\left( \frac{\pi}{3}\right)$.

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