
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
Find the number of ordered pairs  $(a,b)$  such that  $a,b \in \{10,11,\cdots,29,30\}$  and  $\hspace{1cm}$   $GCD(a,b)+LCM(a,b)=a+b$ .

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