
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
In a diagram, there are two overlapping triangles ABC and DEF. Angle A, angle C in triangle ABC, and angle E in triangle DEF are marked as angles 1, 3, and 5 respectively. Similarly, angle B, angle D in triangle DEF, and angle F in triangle ABC are marked as angles 2, 4, and 6 respectively. If each triangle's angles are distinct but still form valid triangles, what is the sum of the measures of angles 1, 2, 3, 4, 5, and 6?

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