
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 2023 AMC 10, students receive $7$ points for each correct answer, lose $1$ point for each incorrect answer, and gain $2$ points for each unanswered problem. Julia decides to attempt the first $28$ problems of the total $30$, leaving the final $2$ unanswered. How many problems must she solve correctly to score at least $150$ points?

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