
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 \( f(x) = \log_{2}(x + 1) \), the graph of \( y = f(x) \) is shifted 1 unit to the left and then the y-coordinates of all points on the graph are stretched to twice their original values (the x-coordinates remain unchanged), resulting in the graph of the function \( y = g(x) \). What is the maximum value of the function \( F(x) = f(x) - g(x) \)?

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