
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 varying rates, taking $15$ seconds to burn the first centimeter, $30$ seconds for the second centimeter, and $15k$ seconds for the $k$-th centimeter. Calculate the height of the candle $\tfrac{T}{2}$ 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}
user