
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 particle starts from the origin in the coordinate plane and moves along the x-axis, jumping 1 unit in either the positive or negative direction each time. If after 5 jumps the particle lands at point (3, 0) (passing through this point multiple times is allowed), then the total number of different ways the particle can move is $\boxed{\text{number}}$; if after 20 jumps the particle lands at point (16, 0) (passing through this point multiple times is allowed), then the total number of different ways the particle can move is $\boxed{\text{number}}$.

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