
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 $f(x) = \log_{2}(x + 1)$.

(1) The graph of the function $f(x)$ is translated 1 unit to the right to obtain the graph of the function $g(x)$. Write the expression for the function $g(x)$.

(2) If the minimum value of the function $y = [g(x)]^{2} - m g(x^{2}) + 3$ in the interval $[1, 4]$ is $2$, find the value of $m$.

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