
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 radio tube can belong to one of three batches with the following probabilities: $p_{1}=0.2, p_{2}=0.3, p_{3}=0.5$. The probability that the tube will operate for a specified number of hours for these batches is respectively: 0.9, 0.8, 0.7. Determine the probability that the radio tube will operate for the specified number of hours.

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