
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
(12 points) Using the six digits 0, 1, 2, 3, 4, 5, complete the following three questions:
(1) If digits can be repeated, how many different five-digit even numbers can be formed?
(2) If digits cannot be repeated, how many different five-digit numbers divisible by 5, with the hundredth digit not being 3, can be formed?
(3) If in the linear equation $ax + by = 0$, $a$ and $b$ can be any two different digits from the given six, how many different lines can be represented by the equation?

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