
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  $k,x,y$  be postive integers. The quotients of  $k$  divided by  $x^2, y^2$  are  $n,n+148$  respectively.( $k$  is divisible by  $x^2$  and  $y^2$ )
(a) If  $\gcd(x,y)=1$ , then find  $k$ .
(b) If  $\gcd(x,y)=4$ , then find  $k$ .

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