
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 lines \(x=\frac{1}{3}y+a\) and \(y=\frac{1}{3}x+b\) intersect at the point \((2,3)\). Determine the value of \(a+b\).
A) $\frac{8}{3}$
B) $4$
C) $\frac{9}{3}$
D) $\frac{10}{3}$

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