
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 with 10 steps. Each time, he jumps either one step up or two steps up. How many different ways are there for Alex to climb the staircase?

b) During descent from the same staircase, Alex jumps over some steps (he may even jump all 10 steps at once). How many different ways are there for him to descend the staircase?

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