
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 chosen on the graph of \( f(x) = \ln(x^2) \), with \( 0 < x_1 < x_2 \). The points \( C \) and \( D \) trisect \(\overline{AB}\), with \( AC < CB \). Through \( C \) a horizontal line is drawn to cut the curve again at \( E(x_3, y_3) \). Find \( x_3 \) if \( x_1 = 1 \) and \( x_2 = 10 \).

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