
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
The 2023 Math Olympiad scores $7$ points for each correct answer, deducts $2$ points for each incorrect answer, and provides $2$ points for each unanswered problem. In this competition, there are $30$ problems total. Emily decides to solve the first $25$ problems and leave the last $5$ unanswered. How many of the first $25$ problems must she solve correctly to score at least $120$ points?

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