
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
From the six digits 0, 1, 2, 3, 4, 5, forming natural numbers without repeating digits,  
find: (1) How many five-digit numbers contain 2 and 3, but they are not adjacent?  
(2) How many six-digit numbers are there in which the digits 1, 2, 3 must be arranged in descending order?

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