
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 $f(x)=2\cos x(\cos x+ \sqrt {3}\sin x)-1$.

(I) Find the minimum value of $f(x)$;

(II) In $\triangle ABC$, angles $A$, $B$, $C$ have opposite sides $a$, $b$, $c$ respectively. If $f( \frac {C}{2})=2$ and $ab=c^{2}$, find $A$.

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