
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
A Tim number is a five-digit positive integer with the following properties:
1. It is a multiple of 15.
2. Its hundreds digit is 3.
3. Its tens digit is equal to the sum of its first three (leftmost) digits.

How many Tim numbers are there?

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