
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 a function $f(x) = x^2 + (\log a + 2)x + \log b$ that satisfies $f(-1) = -2$ and $f(x) \geq 2x$ for all real numbers $x$, determine the values of the real numbers $a$ and $b$.

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