
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
Let $a$ be the number of numbers that satisfy the condition "there is no other number whose absolute value is equal to the absolute value of $a$," $b$ be the number of numbers that satisfy the condition "there is no other number whose square is equal to the square of $b$," and $c$ be the number of numbers that satisfy the condition "there is no other number that, when multiplied by $c$, results in a product greater than 1." Then, $a+b+c=$ ?

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