
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 rays OA and OB form a right angle. A seventh-grader, Petya, drew rays OC and OD inside this angle such that they form an angle of $10^\circ$, and then calculated all the acute angles between any pairs of the drawn rays (not just adjacent ones). It turned out that the sum of the largest and the smallest of the found angles is $85^\circ$. Find the sizes of the three angles into which the right angle is divided by the rays OC and OD.

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