
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
Consider a grid with width 7 and height 6. How many 11-step paths are there from point $E$ to point $G$ which pass through point $F$? Assume $E$ is at the top left corner, $F$ is 4 steps to the right and 2 steps down from $E$, and $G$ is 3 steps to the right and 3 steps down from $F$.

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