
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
Among the numbers formed by the digits 1, 2, 3, 4, 5, 6 without repetition, find:  
(1) The number of six-digit even numbers;  
(2) The number of six-digit numbers where three even numbers are not adjacent to each other;  
(3) The number of six-digit numbers that have exactly two even numbers adjacent to each other;  
(4) The number of six-digit numbers where odd digits are arranged from left to right in ascending order.

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