
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
Consider a $3\times3$ grid where each point is one unit away from its nearest vertical and horizontal neighbors.

[No diagram, but imagine a 3 by 3 grid, each point spaced 1 unit apart]

Find a growing path of distinct points, where each subsequent move has a strictly increasing integral distance from the last. Calculate $m$, the maximum number of points in such a growing path, and $r$, the number of such maximum-length growing paths. Compute the product $mr$.

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