
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 large candle is 150 centimeters tall. It burns down at a varying rate: the candle takes 15 seconds to burn down the first centimeter from the top, 30 seconds for the second centimeter, and \( 15k \) seconds for the \( k \)-th centimeter. Compute the height of the candle in centimeters \( \frac{T}{2} \) seconds after it is lit, where \( T \) is the total time for the candle to burn down completely.

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