
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 quadrilateral is intersected by two diagonals, dividing it into four smaller triangles labeled from 1 to 4. Assume that the intersection of the diagonals is a point such that no side of the quadrilateral passes through this point. How many degrees are in the sum of the measures of the angles at the vertices of the smaller triangles numbered 1 through 4, where each vertex's angle is part of the quadrilateral or a diagonal intersection?

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