
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 a room, there are 10 lamps. Petya said, "There are 5 lamps turned on in this room." Vasya replied to him, "You are wrong." And he added, "There are three lamps turned off in this room." Kolya said, "An even number of lamps are turned on." It turned out that out of the four statements made, only one is true. How many lamps are turned on?

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