
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
Let $G$ be the centroid of triangle $\triangle ABC$. Line $PQ$ passes through the centroid $G$ and satisfies
$$
\begin{array}{l}
\overrightarrow{C P} = m \overrightarrow{C A}, \overrightarrow{C Q} = n \overrightarrow{C B}.
\end{array}
$$
Then $\frac{1}{m} + $\frac{1}{n}$ equals:

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