
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 mathematics test with 90 problems (20 arithmetic, 40 algebra, and 30 geometry), Tori answered $80\%$ of arithmetic, $50\%$ of algebra, and $70\%$ of geometry problems correctly. However, she failed to pass the test as she scored less than $65\%$ overall. How many additional correct answers were required for her to achieve a $65\%$ passing grade?

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