
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 $x = \frac 13y + a$ and $y = \frac 13x + b$ intersect at the point $(3,1)$. What is $a + b$?
A) $\frac{3}{8}$
B) $1$
C) $\frac{8}{7}$
D) $\frac{8}{3}$
E) $\frac{9}{4}$

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