
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 $f(x)=\sin (x+ \frac{7\pi}{4})+\cos (x- \frac{3\pi}{4})$, where $x\in R$.
(1) Find the smallest positive period and the minimum value of $f(x)$;
(2) Given that $f(\alpha)= \frac{6}{5}$, where $0 < \alpha < \frac{3\pi}{4}$, find the value of $f(2\alpha)$.

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