
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 tall candle is \(100\) centimeters in height. The candle burns at a varying rate, starting slowly and accelerating as it burns down. The burning time for the \(k\)-th centimeter from the top is \(5k\) seconds. Determine the height of the candle in centimeters \( \frac{T}{2}\) seconds after it is lit, where \(T\) is the total time the candle takes to burn completely.

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