
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
A line $x = k$ intersects the graphs of $y = \log_5 x$ and $y = \log_5 (x + 8)$. The distance between the points of intersection is $1$. Express $k$ in the form $a + \sqrt{b}$, where $a$ and $b$ are integers, and find $a + b$.

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