
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 $\overrightarrow{m}=(\sin x,\cos x)$, $\overrightarrow{n}=( \frac { \sqrt {3}}{2}, \frac {1}{2})$, $x\in R$, and the function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}$:

1. Find the maximum value of $f(x)$;
2. Solve the inequality $f(x)\geqslant \frac {1}{2}$ with respect to $x$.

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