
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 festival candle is 150 centimeters tall. Initially, it burns faster but slows down significantly as it burns down. It takes $10k^2$ seconds for the \(k\)-th centimeter to burn down, where \(k\) is the centimeter index from the top. Calculate the height of the candle when half of the total burning time has elapsed.

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