
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 $P(x_1, y_1)$ and $Q(x_2, y_2)$ are chosen on the graph of $f(x) = \log_2 x$, with $0 < x_1 < x_2$. The points $R$ and $S$ trisect $\overline{PQ}$, with $PR < RQ$. A horizontal line is drawn from $R$ to cut the curve at $T(x_4, y_4)$. Find $x_4$ if $x_1 = 4$ and $x_2 = 16$.

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