
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 palace is shaped like a square and divided into $2003 \times 2003$ rooms, similar to the squares on a large chessboard. There is a door between two rooms if and only if they share a wall. The main entrance allows entry into the palace from the outside into the room located at the northwest corner. A person enters the palace, visits some rooms, and then exits the palace through the entrance, returning to the northwest corner for the first time. It turns out this person visited each of the other rooms exactly 100 times, except for the room located at the southeast corner. How many times has the visitor been in the southeast corner room?

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