
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
In five boxes, there are balls identical in weight and size. In two boxes, there are 6 blue and 4 red balls (this is box composition \( H_{1} \)). In two other boxes (composition \( H_{2} \)), there are 8 blue and 2 red balls. In one box (composition \( H_{3} \)), there are 2 blue and 8 red balls. A box is randomly selected, and a ball is drawn from it. The drawn ball turned out to be blue. What is the probability that the blue ball was drawn from a box of the first composition?

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