
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
The blue parabola shown is the graph of the equation $x = dy^2 + ey + f$. The vertex of this parabola is $(2, -3)$, and it passes through the point $(7, 0)$. Determine the value of $f$.

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