
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
Based on the table below:

| $x$ | $-3$ | $-2$ | $-1$ | $\ldots $ | $4$ | $5$ | $6$ |
|-----|------|------|------|-----------|-----|-----|-----|
| $x^{2}-bx-5$ | $13$ | $5$ | $-1$ | $\ldots $ | $-1$ | $5$ | $13$ |

Determine the range of solutions for the equation $x^{2}-bx-5=0$.

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