
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
Two points $A(x_1, y_1)$ and $B(x_2, y_2)$ are positioned on the graph of $f(x) = \ln x$, where $0 < x_1 < x_2$. The point $C$ divides the segment $\overline{AB}$ in a ratio of 1 to 3 (from $A$ to $B$). Through point $C$ a horizontal line is drawn which intersects the curve again at $E(x_3, y_3)$. Calculate $x_3$ if $x_1 = 2$ and $x_2 = 32$.

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