
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
For the anniversary of the Saint Petersburg Mathematics Olympiad, the mint produced three commemorative coins. One coin is normal, the second coin has two heads, and the third coin has two tails. Without looking, the director of the mint randomly selected one of these three coins and tossed it. It landed heads up. What is the probability that the other side of this coin is also heads?

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