
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 museum has 7 adjacent exhibition rooms. A guard starts walking to the first room, then to the second room... after reaching the seventh room, he turns back and goes to the sixth room, then to the fifth room... Every time he enters a room, he switches the light in that room on or off. If all 7 rooms are illuminated at the beginning, how many rooms will still be illuminated after he has walked through 100 rooms?

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