
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
A frog starts at the point (1, 1) in the Cartesian coordinate system and can jump in the following two ways:  
① It can jump from any point (a, b) to the point (2a, b) or (a, 2b);  
② For the point (a, b), if a > b, it can jump from (a, b) to (a - b, b); if a < b, it can jump from (a, b) to (a, b - a).  
For example, following the above jumping methods, the frog can reach the point (3, 1), and one of the jumping paths is:  
(1, 1) → (2, 1) → (4, 1) → (3, 1).  
Please consider: Can the frog reach the following points according to the specified jumping methods? If yes, please provide the path from the point (1, 1) to the specified point; if no, please explain why.  
(1) (3, 5); (2) (12, 60); (3) (200, 5); (4) (200, 6).

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