
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 the function $f(x)= \overrightarrow{m} \cdot \overrightarrow{n}$, where $\overrightarrow{m}=(2\cos x,1)$, $\overrightarrow{n}=(\cos x, \sqrt {3}\sin 2x)$, and $x\in R$.
1. Find the interval where $f(x)$ is monotonically increasing.
2. If the inequality $f(x)-m > 0$ holds for any $x\in[0, \frac {π}{2}]$, find the range of values for the real number $m$.

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