
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 that $x\in R$, vector $\overrightarrow{OA}=(a\cos ^{2}x,1)$, $\overrightarrow{OB}=(2, \sqrt {3}a\sin (2x-a))$, and $f(x)= \overrightarrow{OA}\cdot \overrightarrow{OB}$, where $a\neq 0$.
(I) Find the analytical expression of function $f(x)$, and determine the interval where $f(x)$ is monotonically increasing when $a > 0$.
(II) When $x\in[0, \dfrac {\pi}{2}]$, the maximum value of $f(x)$ is $5$, find the value of $a$.

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