
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
The diagram shows a $5\times5$ rectangular array of points, each of which is $1$ unit away from its nearest neighbors. Define a growing path to be a sequence of distinct points of the array where the distance between consecutive points of the sequence is strictly increasing. Determine the maximum possible number of points in a growing path ($m$), and the corresponding number of such growing paths having exactly $m$ points ($r$). Compute the product $mr$.

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