
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
Persons A, B, and C set out from location $A$ to location $B$ at the same time. Their speed ratio is 4: 5: 12, respectively, where A and B travel by foot, and C travels by bicycle. C can carry one person with him on the bicycle (without changing speed). In order for all three to reach $B$ at the same time in the shortest time possible, what is the ratio of the walking distances covered by A and B?

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