
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 $f(x)=\sin x+\cos x$, where $x\in \mathbb{R}$.

  (I) Find the value of $f\left( \frac{\pi}{2}\right)$;

  (II) Find the smallest positive period of the function $f(x)$;

  (III) Find the minimum value of the function $g(x)=f\left(x+ \frac{\pi}{4}\right)+f\left(x+ \frac{3\pi}{4}\right)$.

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