
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
Given the function f(x) = -2alnx + 2(a+1)x - x² (a > 0).

1. Find the value of the real number a if the tangent line of the function f(x) at the point (2, f(2)) is parallel to the line x - y + 1 = 0.
2. Discuss the monotonicity of the function f(x).
3. Find the maximum value of the real number a + b if the function f(x) ≥ -x² + 2ax + b always holds true in the definition domain of the function f(x).

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