
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 system, $A(1,1)$, $B(2,3)$, $C(s,t)$, $P(x,y)$, $\triangle ABC$ is a right isosceles triangle with $B$ as the right angle vertex.<br/>$(1)$ Find the point $C(s,t)$;<br/>$(2)$ Let point $C(s,t)$ be a point in the first quadrant. If $\overrightarrow{AP}=\overrightarrow{AB}-m\overrightarrow{AC}$, where $m\in R$, what is the value of $m$ when point $P$ is in the second quadrant?

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