
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
In the Cartesian coordinate plane $(xOy)$, point $P$ is a moving point on the graph of the function $f(x) = \ln x (x \geqslant 1)$. The tangent line $l$ to the graph at point $P$ intersects the $x$-axis at point $M$. The line perpendicular to $l$ passing through point $P$ intersects the $x$-axis at point $N$. Let $t$ be the $x$-coordinate of the midpoint of segment $MN$. Find the maximum value of $t$.

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