
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
For transportation between points located hundreds of kilometers apart on the Earth's surface, people of the future will likely dig straight tunnels through which capsules will travel frictionlessly under the influence of Earth's gravity. Let points \( A, B, \) and \( C \) lie on the same meridian, with the surface distance from \( A \) to \( B \) related to the surface distance from \( B \) to \( C \) in the ratio \( m : n \). A capsule travels through the tunnel \( AB \) in approximately 42 minutes. Estimate the travel time through tunnel \( AC \). Provide the answer in minutes.

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