
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 11-step paths are there from \( E \) to \( G \) which pass through \( F \)? Assume \( E \) is at the top left, \( G \) is at the bottom right, and \( F \) is now positioned such that it requires 4 steps from \( E \) and 6 more steps from \( F \) to \( G \) on a grid.

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