
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
Clarabelle wants to travel from  $(0,0)$  to  $(6,2)$  in the coordinate plane. She is able to move in one-unit steps up, down, or right, must stay between  $y=0$  and  $y=2$  (inclusive), and is not allowed to visit the same point twice. How many paths can she take?

*Proposed by Connor Gordon*

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