
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
Let \(a, b, c\) be real numbers, all greater than 2, such that
\[
\frac{(a - 1)^2}{b + c + 1} + \frac{(b + 1)^2}{c + a - 1} + \frac{(c + 5)^2}{a + b - 5} = 49.
\]

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