
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
The graphs of \( y = -(x-a)^2 + b \) and \( y = (x-c)^2 + d \) intersect at the points \( (3,6) \) and \( (7,2) \). Determine the value of \( a+c \).

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