
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 $\overrightarrow{a}=(5 \sqrt {3}\cos x,\cos x)$, $\overrightarrow{b}=(\sin x,2\cos x)$, let $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}+| \overrightarrow{b}|^{2}$.
(1) Find the period, maximum, and minimum values of $f(x)$;
(2) Find the interval(s) on which $f(x)$ is increasing on $[0,π]$.

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