
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 $f(x)=\sin (x+ \frac{7}{4}π)+\cos (x- \frac{3}{4}π)$, where $x\in R$
(1) Find the smallest positive period and minimum value of $f(x)$
(2) Given $\cos (β-α)= \frac{4}{5}$, $\cos (β+α)=- \frac{4}{5}$, $0 < α < β\leqslant \frac{π}{2}$, find the value of $[f(β)]^{2}$.

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