
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
The inner chambers of Sultan Ibrahim ibn Said's palace consist of 100 identical square rooms arranged in a $10 \times 10$ grid. If two rooms share a common wall, there must be exactly one door in that wall. If a wall is an outer wall (end wall), there must be exactly one window in it. How can we count the total number of windows and doors in the chambers of Ibrahim ibn Said?

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