
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 an 11-step path from point $H$ to point $J$ on a grid, passing through point $K$. You are provided with this new configuration of points on the grid: $H$ is at (0,0), $K$ is at (4,3), and $J$ is at (6,5). How many different 11-step paths exist from $H$ to $J$ passing through $K$? Assume only moves to the right or downward are allowed.

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