
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
Given the function $f(x)=\ln x-2$

(1) Find the equation of the tangent line at point $P(1,-2)$?

(2) Find a point $Q$ on the function $f(x)=\ln x-2$ such that the distance from $Q$ to line $l:x-2y+3=0$ is minimized. Calculate the coordinates of point $Q$ that satisfies this condition?

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