
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
An ant walks from the bottom left corner of a \( 10 \times 10 \) square grid to the diagonally-opposite corner, always walking along grid lines and taking as short a route as possible. Let \( N(k) \) be the number of different paths that the ant could follow if it makes exactly \( k \) turns. Find \( N(6) - N(5) \).

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