
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 a break, a fly entered the math 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 started moving along 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 segment at its midpoint.

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