
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 $\overrightarrow{a}=(\sin x,\cos x)$, $\overrightarrow{b}=(\cos x,\cos x)$, and the function $f(x)= \overrightarrow{a}\cdot ( \overrightarrow{a}+ \overrightarrow{b})- \frac {3}{2}$,

1. Find the smallest positive period and the maximum value of the function $f(x)$.
2. Find the interval(s) where the function $f(x)$ is strictly increasing.

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