
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 values of the positive integer  $k$  that has the property:
There are no positive integers  $a,b$  such that the expression  $A(k,a,b)=\frac{a+b}{a^2+k^2b^2-k^2ab}$  is a composite positive number.

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