
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
Alice is jogging north at a speed of 6 miles per hour, and Tom is starting 3 miles directly south of Alice, jogging north at a speed of 9 miles per hour. Moreover, assume Tom changes his path to head north directly after 10 minutes of eastward travel. How many minutes after this directional change will it take for Tom to catch up to Alice?

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