
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 a computer game, each game session yields an integer score. The game's creator keeps a list of the top 30 scores, annotated with decreasing scores from 30 down to 1. Our score from a game session, under our personal name, will be added to the list if it is higher than the current lowest score on the list, which will then be removed. In case of equal scores, the most recently added score is removed. The ranking is done from the bottom up, so we only move up on the list past scores that we exceed. Assuming we add our score to the list after each game, how many games must we play to ensure our name appears next to all the scores on the list?

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