
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 $\overrightarrow{a}=( \sqrt {3}\sin x,1)$ and $\overrightarrow{b}=(\cos x,2)$,

1. If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find the value of $\tan 2x$.
2. If $f(x)=( \overrightarrow{a}- \overrightarrow{b})\cdot \overrightarrow{b}$, find the interval where $f(x)$ is monotonically increasing.

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