
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 $f(x)=\sin (x+ \frac{5π}{2})\cos (x- \frac{π}{2})-\cos ^{2}(x+ \frac{π}{4}).$
(1) Find the monotonic intervals of $f(x)$;
(2) In acute triangle $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are respectively $a$, $b$, $c$. If $f(\frac{A}{2})=\frac{\sqrt{3}-1}{2}$, $a=1$, find the maximum value of the perimeter of $\triangle ABC$.

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