
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
How many degrees are in the sum of the measures of the nine numbered angles pictured in the diagram? In the diagram, there are three triangles, each sharing sides but not overlapping:
1. Triangle A with angles labeled 1, 2, 3.
2. Triangle B with angles labeled 4, 5, 6.
3. Triangle C, newly added, with angles labeled 7, 8, 9.

Each triangle has its vertices connected such that no vertex lies inside another triangle.

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