
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
Consider a quadrilateral ABCD with diagonals AC and BD intersecting at point P. How many degrees are in the sum of the measures of the eight numbered angles pictured in the resulting four triangles (each triangle formed by the intersection of diagonals with the quadrilateral sides)?

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