
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 $f(x)=\sqrt{3}\sin^{2}(x+\frac{\pi}{4})-\cos^{2}x-\frac{1+\sqrt{3}}{2} (x\in\mathbb{R})$.
(1) Find the minimum value and the minimum positive period of the function $f(x)$;
(2) If $A$ is an acute angle, and vector $\overrightarrow{m}=(1,5)$ is perpendicular to vector $\overrightarrow{n}=(1,f(\frac{\pi}{4}-A))$, find $\cos 2A$.

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