
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 cylindrical glass cup has a wall thickness of $1.5 \mathrm{~mm}$, an internal diameter of $6.6 \mathrm{~cm}$, and an internal height of $10 \mathrm{~cm}$. The thickness of the bottom of the cup is $3 \mathrm{~mm}$. The density of the glass is twice the density of water.

Water is slowly poured into the cup until it is full. Determine and graphically represent the position of the system's center of mass as a function of the height of water in the cup.

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