
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 tube at $0^{\circ}$ is $1 \mathrm{~m}$ long with a cross-sectional area of $1 \mathrm{~cm}^{2}$. When positioned vertically and filled with mercury, how high should the mercury stand so that the distance of the center of gravity of the mercury column from the top of the tube remains constant at any temperature? The volumetric expansion coefficient of the glass is $\frac{1}{38700}$ and for mercury, it is $\frac{1}{5550}$.

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