
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 $f(x)=2\cos^{2}x-2 \sqrt {3}\sin x\sin(x- \frac {π}{2})$, find:

1. The smallest positive period $T$ of $f(x)$;
2. The value of $\frac{b}{a}$ in triangle $ABC$ where sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$, respectively, given that $f(\frac{A}{2})=3$ and the area $S=\frac{1}{4}(a^{2}+c^{2}-b^{2})$.

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