
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 medium-sized candle is $60$ centimeters tall. It burns at a rate such that it takes $5$ seconds to burn down the first centimeter from the top, $10$ seconds for the second centimeter, and in general $5k$ seconds for the $k$-th centimeter, where $k$ is the centimeter number from the top. Determine the height of the candle in centimeters when half of the total burning time has elapsed.

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