
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 $f(x)=a^{x+2}-\frac{2}{3} (a>0, a\neq 1)$, if its graph passes through the point $P(m,n)$, then the maximum value of the function $g(x)=\log_{n}(x^2-mx+4)$ is $\_\_\_\_\_\_\_.$

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