
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 sealed vessel with rigid walls of volume \( V = 1 \) liter contains \( V_1 = 0.45 \) liters of water and dry air at atmospheric pressure \( p_0 = 1.0 \cdot 10^5 \) Pa and temperature \( T_1 = +30^\circ \mathrm{C} \). The vessel is an inverted cone. A thin layer of machine oil separates the water from the air. The vessel is cooled to a temperature \( T_2 = -30^\circ \mathrm{C} \), causing all the water to freeze. The density of water is \( \rho_1 = 1.0 \) g/cm\(^3\) and the density of ice is \( \rho_2 = 0.9 \) g/cm\(^3\). Determine the pressure of the air above the ice. Compare it with atmospheric pressure and explain the result of the comparison.

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