
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
Given 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 $n\in N$, find $f\_{2013}(\frac{\pi}{3})$.

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