
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
Given that Alice is $1.6$ meters tall and her height is increased by $5$ centimeters by her hat and she can reach $50$ centimeters above her head, the ceiling height is $2.8$ meters, and the floor dips down $3$ centimeters, calculate the height of the stool, in centimeters.

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