
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 candle is 150 centimeters tall and burns at a variable rate. It takes $10$ seconds plus an additional $5$ seconds for each centimeter from the top to burn down each subsequent centimeter. If the time taken to burn down the k-th centimeter is $10k + 5$ seconds, calculate how tall the candle is $\frac{T}{2}$ seconds after being 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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