
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 snowdrift with a height of 468 cm decreases by 6 cm in height during the first hour, by 12 cm during the second hour, and by $6k$ cm during the $k$-th hour. Over a certain period $T$, the snowdrift completely melts. What fraction of the snowdrift’s height has melted over the time $\frac{T}{2}$?

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