
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 person climbs a mountain (from the foot of the mountain to the top) at an average speed of $V_{1}$, and descends the mountain (returning to the foot of the mountain) at an average speed of $V_{2}$. From the beginning of the climb to the top of the mountain and immediately descending back to the foot of the mountain, the average speed for the entire journey is $V$. Given that $V_{2} = k V_{1}$, $V = m V_{1}$, and $V = n V_{2}$, find $m$ (expressed as an algebraic expression in terms of $k$) and $m+n$.

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