
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 vectors $\overset{→}{a} =(2\sin x, 1)$, $\overset{→}{b} =(\cos x, 1-\cos 2x)$, and the function $f(x)=\overset{→}{a} \cdot \overset{→}{b} (x\in R)$.

(1) Find the smallest positive period, maximum value, and minimum value of the function $f(x)$;
(2) Find the monotonically increasing interval of the function $f(x)$.

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