
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
Katya and Pasha ask each other four tricky questions and answer them randomly without thinking. The probability that Katya lies in response to any question from Pasha is $\frac{1}{3}$ and does not depend on the question number. Pasha answers Katya’s questions truthfully with a probability of $\frac{3}{5}$, regardless of the question order. After the dialogue, it was revealed that Pasha gave two more truthful answers than Katya. What is the probability that this could have happened?

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