
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
A point starts from the origin on a line and makes \(a\) steps, each step moving one unit to the right, and \(b\) steps, each step moving one unit to the left, in some order, with \(a > b\). The range of the point's walk is defined as the difference between the greatest and smallest coordinates of the point during the entire walk.

a) Find the greatest possible range of the walk.

b) Find the smallest possible range.

c) How many different sequences of the point's movements result in the greatest possible range?

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