
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
Given the digits 0, 1, 2, 3, 4, 5 (a total of six digits), answer the following questions using numbers for the final results:  
(1) How many distinct three-digit even numbers can be formed with these six digits without repetition?  
(2) How many monotonic increasing sequences can be formed by choosing any three different digits from these six?

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