
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
Our school held a math competition with a total of 25 questions and a full score of 100 points. Each correct answer earns 4 points, each wrong answer deducts 1 point, and not answering gives 0 points.  
$(1)$ A student left one question unanswered and scored 86 points in the end. How many questions did the student answer correctly in total?  
$(2)$ If it is required that participants must answer every question and score above or equal to 90 points to be awarded a first prize, how many questions must a participant answer correctly at least to receive the first prize?

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