
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 and Bob live on the same road. At time  $t$ , they both decide to walk to each other's houses at constant speed. However, they were busy thinking about math so that they didn't realize passing each other. Alice arrived at Bob's house at  $3:19\text{pm}$ , and Bob arrived at Alice's house at  $3:29\text{pm}$ . Charlie, who was driving by, noted that Alice and Bob passed each other at  $3:11\text{pm}$ . Find the difference in minutes between the time Alice and Bob left their own houses and noon on that day.

*Proposed by Kevin You*

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