
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
Tom can run to Beth's house in  $63$  minutes.  Beth can run to Tom's house in  $84$  minutes.  At noon Tom starts running from his house toward Beth's house while at the same time Beth starts running from her house toward Tom's house.  When they meet, they both run at Beth's speed back to Beth's house.  At how many minutes after noon will they arrive at Beth's house?

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