
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
Two toads named Gamakichi and Gamatatsu are sitting at the points  $(0,0)$  and  $(2,0)$  respectively. Their goal is to reach  $(5,5)$  and  $(7,5)$  respectively by making one unit jumps in positive  $x$  or  $y$  direction at a time. How many ways can they do this while ensuring that there is no point on the plane where both Gamakichi And Gamatatsu land on?

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