
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
If a number $a$ can be expressed as the sum of squares of two natural numbers (which can be the same), then $a$ is called a "good number".  
(1) Determine how many good numbers there are among the first 10 natural numbers: 1, 2, 3, ..., 9, 10.  
(2) Determine how many good numbers there are among the first 100 natural numbers: 1, 2, 3, ..., 99, 100.

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