
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 \( f(x) = |\lg (x + 1)| \) and real numbers \( a \) and \( b \) with \( a < b \), which satisfy \( f(a) = f\left(-\frac{b + 1}{b + 2}\right) \) and \( f(10a + 6b + 21) = 4 \lg 2 \), find the values of \( a \) and \( b \).

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