
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
Let  $a$  and  $b$  be nonzero real numbers such that  $\tfrac{1}{3a}+\tfrac{1}{b}=2011$  and  $\tfrac{1}{a}+\tfrac{1}{3b}=1$ .  What is the quotient when  $a+b$  is divided by  $ab$ ?

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