
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 collector is deciding how to price a series of unique collectible cards. He assigns a price using the six digits 1, 1, 4, 5, 6, and 6, ensuring that the price does not start with an odd number smaller than 5. How many valid prices can there be?

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