
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 stands on a horizontal tabletop, with the water level inside the glass being at a height $m_{1}$ above the tabletop. Upon tilting the glass so that the plane of its base forms an angle with the tabletop, the water does not spill, and the new water level reaches a height $m_{2}$. How much water is in the glass? How does the result change if we consider that the glass has a thickness of $d_{1}$ at the bottom and $d_{2}$ at the side? Numerical data: $m_{1}=40 \mathrm{~mm}$, $a=25^{\circ}$, $m_{2}=48 \mathrm{~mm}$, $d_{1}=7 \mathrm{~mm}$, and $d_{2}=3 \mathrm{~mm}$.

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