
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
Suppose that  $a, b, c$ , and  $d$  are real numbers simultaneously satisfying $a + b - c - d = 3$  $ab - 3bc + cd - 3da = 4$  $3ab - bc + 3cd - da = 5$ Find  $11(a - c)^2 + 17(b -d)^2$ .

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