
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
To celebrate the anniversary of the St. Petersburg Mathematical Olympiads, the mint produced three commemorative coins. One coin was correct, the second coin had two heads, and the third coin had two tails. The director of the mint randomly selected one of these three coins without looking and flipped it. It landed on heads. What is the probability that the second side of this coin is also heads?

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