
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 $| \overrightarrow{m}|=1$, $| \overrightarrow{n}|=2$, $2 \overrightarrow{m}+ \overrightarrow{n}$ is perpendicular to $\overrightarrow{m}-3 \overrightarrow{n}$, $\overrightarrow{a}=4 \overrightarrow{m}- \overrightarrow{n}$, and $\overrightarrow{b}=7 \overrightarrow{m}+2 \overrightarrow{n}$, find the value of $< \overrightarrow{a}, \overrightarrow{b} >$.

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