
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 passenger train left station $A$ towards station $B$. At the same time, from station $B$ towards station $A$, the "Arrow" train departed. The trains met at station $C$. After the meeting, the passenger train traveled for $b$ hours, while the "Arrow" train traveled for $c$ hours. How much time did each of these trains take for the entire journey between stations $A$ and $B$? It is assumed that the trains' speeds are constant throughout the journey.

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