
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
(The full score of this question is 12 points)

Given the function $f(x) = x^2 + (2 + \log_a)x + \log_b$, and $f(-1) = -2$.

(1) Find the relationship between $a$ and $b$;

(2) If $f(x) \geq 2x$ always holds, find the values of $a$ and $b$.

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