
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 all pairs  $(a, b)$  of positive integers for which  $a + b = \phi (a) +  \phi (b) + gcd (a, b)$ .

Here  $ \phi (n)$  is the number of numbers  $k$  from  $\{1, 2,. . . , n\}$  with  $gcd (n, k) = 1$ .

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