
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]


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Given that the real numbers a, b, c, d satisfy the equation \(\sqrt{a+b+c+d} + \sqrt{a^{2}-2a+3-b} - \sqrt{b-c^{2}+4c-8} = 3\), find the value of \(a - b + c - d\).

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