
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 \( f(x) = \log_{2}(x + 1) \), and as the point \((x, y)\) moves along the graph of \( f(x) \), the point \(\left(\frac{x}{3}, \frac{y}{2}\right)\) moves along the graph of \( y = g(x) \). Find the maximum value of the function \( h(x) = g(x) - f(x) \).

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