
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
A line $l$ passes through the intersection point $A$ of lines $l_{1}: x-y+1=0$ and $l_{2}: 2x+y-1=0$, and has a slope of $k$. This line $l$ intersects with the circle $C: (x-2)^{2}+(y-3)^{2}=1$ at points $M$ and $N$. Find the value of $\overrightarrow{AM}\cdot \overrightarrow{AN}$.

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