
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
During the break, a fly entered the mathematics classroom and began crawling on a poster depicting the graph of a quadratic function $y=f(x)$ with a leading coefficient of 1. Initially, the fly moved exactly along the parabola to the point with an abscissa of 2, but then it started moving in a straight line until it again reached the parabola at the point with an abscissa of 4. Find $f(3)$, given that the line $y=2023x$ intersects the fly's path along the straight line segment at its midpoint.

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