
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
Given the equation $\angle 1 + \angle 2 = 180^\circ$ and the relationship $\angle 3 = 2\angle 4$, find $\angle 4$ in the context where in one triangle, $\angle 1 = 50^\circ$ and $\angle 3 + \angle 4 = 130^\circ$.

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