
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
Vitya Perestukin always incorrectly calculates percentages during surveys: he divides the number of respondents who answered a certain way by the number of all remaining respondents. For instance, in the survey "What is your name?" conducted among 7 Annas, 9 Olgas, 8 Julias, Vitya calculated 50% Julias.

Vitya conducted a survey in his school: what type of triangle has sides of \(3, 4, 5\)? According to his calculations, 5% answered "acute", 5% "obtuse", and 5% "such a triangle does not exist", 50% "right", and the remaining \(a \%\) answered "depends on the geometry". What is \(a\)?



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