
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
Two objects start from points $A$ and $B$, and move towards each other. If the total distance between $A$ and $B$ is $m$ and the product of the individual distances traveled before meeting is $n^2$, determine the polynomial whose roots are the distances traveled by each object from $A$ and $B$ before meeting.

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