
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 \( f(x) = 3x + 4 \), find the expression for the function \( y = g(x) \) under the following conditions:

1. The graph of \( y = g(x) \) is obtained by shifting the graph of \( y = f(x) \) to the left by 1 unit and then down by 2 units.
2. The graph of \( y = g(x) \) is symmetric with respect to the \( y \)-axis compared to the graph of \( y = f(x) \).
3. The graph of \( y = g(x) \) is symmetric with respect to the line \( y = 1 \) compared to the graph of \( y = f(x) \).
4. The graph of \( y = g(x) \) is symmetric with respect to the line \( y = -x \) compared to the graph of \( y = f(x) \).
5. The graph of \( y = g(x) \) is symmetric with respect to the point \( P(a, b) \) compared to the graph of \( y = f(x) \).

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