
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, $\|\overrightarrow{OA}\| = 1,$ $\|\overrightarrow{OB}\| = 2,$ and $\|\overrightarrow{OC}\| = \sqrt{3}.$ Also, $\tan \angle AOC = 3$ and $\angle BOC = 45^\circ.$

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

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