
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 container at $0^{\circ}$ contains $300 \mathrm{~g}$ of water and $50 \mathrm{~g}$ of ice; the weight of the container is $100 \mathrm{~g}$ and the specific heat capacity of the container's material is 0.5. How many grams of $100^{\circ}$ water vapor need to be introduced into the container for the final temperature to be $20^{\circ}$?

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