
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
On a larger grid where each block is 1 unit by 1 unit, suppose we wish to walk from point $A$ to point $B$ but must pass through point $C$. The grid dimensions have increased to 7 units in width and 6 units in height. Starting at $A$ (bottom-left corner), passing through $C$ (positioned at 3 units to the right and 2 units up from $A$), and finishing at $B$ (top-right corner), how many different paths can we take if each path is exactly 13 units long? You must stay on the grid lines and may only move right or up.

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