
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
You can determine all 4-ples  $(a,b, c,d)$  of real numbers, which solve the following equation system  $\begin{cases} ab + ac = 3b + 3c 
bc + bd = 5c + 5d 
ac + cd = 7a + 7d 
ad + bd = 9a + 9b \end{cases} $ 

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