
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 quadratic function $f(x) = -x^2 + 4x + 3$  
(1) Identify its axis of symmetry and the coordinates of its vertex;  
(2) Explain how its graph is obtained by translating the graph of $y = -x^2$;  
(3) If $x \in [1, 4]$, find the maximum and minimum values of the function $f(x)$.

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