
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
Let $f(x) = |\lg(x+1)|$, where $a$ and $b$ are real numbers, and $a < b$ satisfies $f(a) = f(- \frac{b+1}{b+2})$ and $f(10a + 6b + 21) = 4\lg2$. Find the value of $a + b$.

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