
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 the parabola $y=x^{2}+2x-3$ intersects the line $l_{1}$: $y=-x+m$ at points $A$ and $C$, and the line $l_{2}$ is symmetric with respect to the axis of symmetry of the parabola. Line $l_{2}$ intersects the parabola at points $B$ and $D$, where points $A$ and $D$ are above the $x$-axis, and points $B$ and $C$ are below the $x$-axis. If $AC \cdot BD = 26$, then the value of $m$ is ______.

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