
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 vectors $\overrightarrow{m}=(-2\sin (π-x),\cos x)$, $\overrightarrow{n}=( \sqrt {3}\cos x,2\sin ( \frac {π}{2}-x))$, and function $f(x)=1- \overrightarrow{m}⋅ \overrightarrow{n}$:
1. Find the range of function $f(x)$ when $x \in [0, \frac {π}{2}]$;
2. Find the interval where $f(x)$ is monotonically increasing when $x \in [0,π]$.

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