
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 that the parabola $y=ax^{2}+bx+3$ intersects the $x$-axis at points $A(-1,0)$ and $B(3,0)$.<br/>$(1)$ Find the analytical expression of the parabola;<br/>$(2)$ A line parallel to the $x$-axis passing through point $D(0,\frac{7}{4})$ intersects the parabola at points $E$ and $F$. Find the length of $EF$.

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