
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
A and B depart simultaneously from location $A$ and travel at a constant speed towards location $B$, while C departs from location $B$ and travels at a constant speed towards location $A$. After 20 minutes, A meets C. Then, A immediately turns around, meets B after 10 minutes, and then turns around again to head towards location $B$. When A reaches location $B$, B has passed the midpoint between locations $A$ and $B$ by 105 meters, while C is still 315 meters away from location $A$. Determine the ratio of A's speed to B's speed and the distance between locations $A$ and $B$.

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