
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 $DOG$, we have $\angle{DGO}=\angle{DOG}$ and $\angle{DOG}=50^\circ$. If $\overline{OX}$ bisects $\angle{DOG}$, then what is the measure of $\angle{DXG}$? [asy]
/* Modified problem based on an original style */
draw((0,0)--(.5,2)--(1,0)--cycle);
draw((1,0)--(.25,1));
label("$X$", (.25,1), W);
label("$G$", (0,0), SW);
label("$O$", (1,0), SE);
label("$D$", (.5,2), N);
[/asy]

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