
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
In the game of Woogle, dropping \(n\) woogles gives a score equal to the sum of the first \(n\) positive integers. Eating \(n\) woogles, however, now earns \(15n\) points. What is the least number of woogles for which dropping them will earn more points than eating them?

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