
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 $5 \times 5$ grid of points, each spaced 1 unit apart. Define a growing path as before, but now the path can have at most one directional change (a turn). Calculate the maximum number of points in such a path (let's denote it by $m$) and the number of such maximum paths ($r$). Determine the product $mr$.

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