
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
How many paths are there from point $A$ to point $B$ in a $7 \times 6$ grid, if every step must be up or to the right, and you must not pass through the cell at position $(3,3)$?
[asy]size(4cm,4cm);int w=7;int h=6;int i;pen p=fontsize(9);for (i=0; i<h; ++i){draw((0,i) -- (w-1,i));}for (i=0; i<w; ++i){draw((i, 0)--(i,h-1));}label("$A$", (0,0), SW, p);label("$B$", (w-1,h-1), NE, p);fill((3,3)--(4,3)--(4,4)--(3,4)--cycle, grey);[/asy]

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