
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 $\overrightarrow{a}=( \frac { \sqrt {3}}{2}\sin x,2\cos x)$ and $\overrightarrow{b}=(2\cos x, \frac {1}{2}\cos x)$, let the function $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}+m$.
(1) Find the smallest positive period of the function $f(x)$.
(2) If the minimum value of the function $f(x)$ is $1$, find the value of $m$ and then find the maximum value of $f(x)$ and the equation of the symmetry axis of the graph.

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