
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 vectors $\overset{→}{a}=(\sin x, \frac{1}{2})$, $\overset{→}{b}=( \sqrt{3}\cos x+\sin x,-1)$, and the function $f(x)= \overset{→}{a} \cdot \overset{→}{b}$,

1. Find the smallest positive period of the function $f(x)$.
2. Find the maximum and minimum values of $f(x)$ on the interval $[\frac{\pi}{4},\frac{\pi}{2}]$.

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