
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) There are two ropes. If either one of them is ignited from one end, it will burn for an hour. The ropes burn unevenly. For example, it cannot be guaranteed that half of the rope will burn in 30 minutes. Using these two ropes, how can you measure a 15-minute interval?

b) How many different time intervals (including zero) can be measured using three such ropes?

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