
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) Determine the smallest positive period of the function $f(x)$.
- (III) Calculate 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}
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