
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
Given that the volume of pool \(M\) is 1.5 times that of pool \(N\), there are three water pipes \(A\), \(B\), and \(C\). Pipe \(A\) alone can fill pool \(M\) in 5 hours; pipe \(B\) alone can fill pool \(N\) in 5 hours; pipe \(C\) alone can fill pool \(N\) in 6 hours. If pipes \(A\), \(B\), and \(C\) are opened simultaneously, with \(A\) always filling pool \(M\), \(C\) always filling pool \(N\), and \(B\) starting by filling pool \(M\) and then switching to fill pool \(N\), the two pools are both filled exactly at the same time. How many hours does pipe \(B\) fill pool \(M\)?

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