
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
Determine the number of paths from  $A$  to  $B$  on the picture that go along gridlines only, do not pass through any point twice, and never go upwards?
![Image](https://cdn.artofproblemsolving.com/attachments/0/2/87868e24a48a2e130fb5039daeb85af42f4b9d.png)

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