
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 following four propositions:
1. The solution set of the inequality $x^2 - 4ax + 3a^2 < 0$ is $\{ x | a < x < 3a \}$;
2. If the function $y = f(x + 1)$ is an even function, then the graph of $y = f(x)$ is symmetric about $x = 1$;
3. If the solution set of the inequality $|x-4| + |x-3| < a$ is empty, then $a \leq 1$ must hold;
4. The graph of the function $y = f(x)$ has at most one intersection point with the line $x = a$.
Identify the correct propositions.

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