
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
Let the vector $\overrightarrow {a}=(\sin x,  \sqrt {3}\cos x)$, and the vector $\overrightarrow {b}=(\cos x, \cos x)$, where $(0<x<\frac{\pi}{2})$.
(1) If $\overrightarrow {a} \| \overrightarrow {b}$, find the value of $\tan x$;
(2) Determine the period and the maximum value of the function $f(x) = \overrightarrow {a}\cdot\overrightarrow {b}$, as well as the corresponding value of $x$.

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