
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
Two identical isosceles triangles are positioned such that their bases are on the same line but they do not touch each other. The vertex angles of the triangles are each $40^\circ$. The triangles are rotated such that their equal sides are facing each other and the vertices of these angles are $4$ units apart. What is the sum of the angles at the vertices facing each other?

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