
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 last four games of a soccer season, a player scored $25$, $15$, $10$, and $22$ goals, respectively. Her goals-per-game average was higher after twelve games than it was after the first eight games. If her average after thirteen games was greater than $20$, determine the least number of goals she could have scored in the thirteenth game.

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