
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
As shown in the diagram, through point \( D \) draw \( D O \) bisecting \( \angle A D C \). Through point \( B \) draw \( B O \) bisecting \( \angle A B C \), with \( B O \) and \( D O \) intersecting at point \( O \). Given that \( \angle A = 35^\circ \) and \( \angle O = 42^\circ \), find \( \angle C \).

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