
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
The system of equations 
$a+bc=1,$
$b+ac=1,$
$c+ab=1,$
has how many real solutions for $a$, $b$, and $c$.

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