
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
A line passing through the centroid $G$ of $\triangle OAB$ intersects $OA$ and $OB$ at points $P$ and $Q$ respectively. Given that $\overrightarrow{OP} =m\overrightarrow{OA} $ and $\overrightarrow{OQ} =n\overrightarrow{OB} $, where $m$ and $n$ are real numbers, find the value of $\frac{1}{n} +\frac{1}{m}$.

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