
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) State its axis of symmetry and the coordinates of the vertex;
(2) Explain how its graph is obtained from the graph of $y=-x^{2}$ through translation;
(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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