
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 triangle $ABC$, the sides are tangent to a circle with center $D$. Given $\angle BAC = 70^\circ$ and $\angle ABC = 52^\circ$, find $\angle BDC$, in degrees.
[asy]
unitsize(1.0 cm);
pair A, B, C, D;
A = (2.43,3.46);
B = (0,0);
C = (4.43,0);
D = incenter(A,B,C);
draw(A--B--C--cycle);
draw(incircle(A,B,C));
draw(C--D);
label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, N);
[/asy]

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