
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 triangle with vertices A, B, and C (triangle ABC), where $m\angle CAB = 85^\circ$, $m\angle ABC = 40^\circ$, and $m\angle BCA = 55^\circ$, a line through B intersects AC at point D such that $\angle ABD = 30^\circ$. What is the measure of angle $\angle DBC$?

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