
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) Alex is climbing a staircase that has 10 steps. Each time, he can jump up either one step or two steps. In how many ways can Alex climb the staircase?

b) When descending the same staircase, Alex can skip over some steps (he might even skip all 10 steps). In how many ways can he descend this staircase?

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