
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 circle has center at $(2, -3)$ and radius $10$, while another circle has center at $(-4, 7)$ with radius $6$. The line passing through the two intersection points of these circles has the equation $x + y = c$. Find the value of $c$.
A) 6  
B) 9  
C) $\frac{26}{3}$  
D) 12

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