
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
In the diagram below, $\|\overrightarrow{OA}\| = 2,$ $\|\overrightarrow{OB}\| = 2,$ and $\|\overrightarrow{OC}\| = 2 \sqrt{3}.$ Also, $\tan \angle AOC = 3$ and $\angle BOC = 60^\circ.$

There exist constants $p$ and $q$ so that
\[
\overrightarrow{OC} = p \overrightarrow{OA} + q \overrightarrow{OB}.
\]
Enter the ordered pair $(p,q)$.

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