
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
Determine all 4-tuples ( $a, b,c, d$ ) of real numbers satisfying the following four equations:  $\begin{cases} ab + c + d = 3 
bc + d + a = 5 
cd + a + b = 2 
da + b + c = 6 \end{cases}$ 

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