
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
Farmer Tim starts walking from the origin following the path \((t, \sin t)\) where \(t\) is the time in minutes. Five minutes later, Alex enters the forest and follows the path \((m, \cos t)\) where \(m\) is the time since Alex started walking. What is the greatest distance between Alex and Farmer Tim while they are walking these paths?

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