
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
Let  $s(n)$  be the number of 1's in the binary representation of  $n$ . Find the number of ordered pairs of integers  $(a,b)$  with  $0 \leq a < 64, 0 \leq b < 64$  and  $s(a+b) = s(a) + s(b) - 1$ .

*Author:Anderson Wang*

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