
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 unique candle is 150 centimeters tall. Each centimeter burns for a time given by $T_k = 1510 - 10k$ seconds for the $k$-th centimeter from the top. Calculate the remaining height of the candle $\frac{3T}{4}$ seconds after it has been lit.

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