
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
Find all real quadruples  $(a,b,c,d)$  satisfying the system of equations  $$ \left\{ \begin{array}{ll}
ab+cd = 6 
ac + bd = 3 
ad + bc = 2 
a + b + c + d = 6.
\end{array} \right.	 $$  

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