
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 fraction $\frac{{2x+a}}{{x-b}}$ (where $a$ and $b$ are constants) satisfies the information in the table below:

| $x$ value | $2$   | $0.5$ | $c$   |
|-----------|-------|-------|-------|
| Fraction value | undefined | $0$ | $3$ |

Find the value of $c$.

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