
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 graph of the function $f(x) = \log_2 x$ is shifted 1 unit to the left, and then the part below the $x$-axis is reflected across the $x$-axis to obtain the graph of function $g(x)$. Suppose real numbers $m$ and $n$ ($m < n$) satisfy $g(m) = g\left(-\frac{n+1}{n+2}\right)$ and $g(10m+6n+21) = 4\log_2 2$. Find the value of $m-n$.

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