
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
A circle inscribed in $\triangle ABC$ is tangent to each side at points lying on the extensions of sides $AB$, $BC$, and $CA$. Suppose the angles at the points where the inscribed circle is tangent to the sides $BC$, $CA$, and $AB$ measure $120^\circ$, $130^\circ$, and $\theta^\circ$ respectively. What is $\theta$?

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