
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 Frood, dropping $n$ froods gives a score equivalent to the sum of the first $n$ positive integers. Eating $n$ froods earns $5n$ points. Determine the smallest number of froods $n$ for which dropping them gives more points than eating them.

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