
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 \( f(x) = \ln (a x + b) + x^2 (a \neq 0) \):
1. If the equation of the tangent line to the curve \( y = f(x) \) at the point \( (1, f(1)) \) is \( y = x \), find the values of \( a \) and \( b \).
2. If \( f(x) \leqslant x^2 + x \) always holds, find the maximum value of \( ab \).

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