
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle of 30° between them, and $|\overrightarrow{a}|= \sqrt{3}$, $|\overrightarrow{b}|=1$. Let $\overrightarrow{m}= \overrightarrow{a}+ \overrightarrow{b}$ and $\overrightarrow{n}= \overrightarrow{a}- \overrightarrow{b}$, find the projection of vector $\overrightarrow{m}$ on the direction of vector $\overrightarrow{n}$.

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