
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) There are 5 different traditional Chinese paintings, 2 different oil paintings, and 7 different watercolor paintings.  
(1) How many different ways are there to choose one painting from each of these categories (traditional Chinese, oil, and watercolor) to decorate a room?  
(2) How many different ways are there to choose two paintings of different types to decorate a room?

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