
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 positive integer is called "balanced" if it has four digits, and one of these digits is equal to the average of the other three. For example, the number 2631 is balanced because 3 is the average of 2, 6, and 1; 4444 is also balanced because 4 is the average of 4, 4, and 4.

a) Find the three smallest balanced numbers.

b) How many balanced numbers are there that are less than 2014?

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