
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
The function $f(x)$ is defined as follows:
$$f(x)= \begin{cases} \sin{x}, & 0<x<1 \\ \cos{x}, & 1 \leq x \leq \sqrt{2} \\ \tan{x}, & x > \sqrt{2} \end{cases}$$
Find the value of $f(\frac{\pi}{3})$.

A) $\frac{\sqrt{3}}{2}$
B) $\frac{\sqrt{3}}{3}$
C) $\frac{1}{2}$
D) $\sqrt{3}$

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