
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 a quadratic function $f(x) = x^2 - ax + 3$, it holds true that for any real number $x$, $f(4-x) = f(x)$.
(1) Determine the value of the real number $a$;
(2) Find the range of the function $f(x)$ within the interval $[0,3]$;
(3) Describe the transformation required to obtain the graph of the function $y = x^2$ from the graph of the quadratic function $y = f(x)$.

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