
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
Point $D$ is on side $AC$ of triangle $ABC$, with $\angle ABD = 25^\circ$ and $\angle DBC = 40^\circ$. $\angle ACB = 30^\circ$. What is the measure of angle $BAC$, in degrees?

[asy]
draw((-43,0)--(43,0)--(43,40)--cycle);
draw((-4,0)--(43,40));
draw((39,4)--(39,0));
draw((39,4)--(43,4));
draw((-1,36)--(22.5,26),Arrow);
label("$25^\circ$",(5,36),W);
label("$40^\circ$",(34,30),S);
label("D",(43,0),S);
label("A",(-43,0),W);
label("B",(43,40),N);
label("C",(0,0),E);
[/asy]

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