
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
Thoroughly purified water can be supercooled to temperatures below $0^\circ$C. However, if a small ice crystal is dropped into it, the water begins to freeze immediately. What fraction of the supercooled water at $-10^\circ$C contained in a thermos will freeze if a small ice crystal is dropped into it? The specific heat capacity of water is $c=4200$ J/(kg·K), and the latent heat of fusion of ice is $\lambda=330$ kJ/kg.

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