
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 motorboat departed from dock A downstream. Simultaneously, a boat departed from dock B upstream towards the motorboat. After some time, they met. At the moment of their meeting, a second boat departed from B and after some time met the motorboat. The distance between the points of the first and second meetings is $\frac{56}{225}$ of the distance AB. The flow velocities, the motorboat, and the boats' speeds are constant (the boats' speeds are the same), and the ratio of the motorboat's speed to the boat's speed is $2:3$. What fraction of the distance AB had the motorboat traveled by the time it met the second boat?

Answer: $\frac{161}{225}$ or $\frac{176}{225}$.

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