
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
Let  $I$  be the center of the incircle of non-isosceles triangle  $ABC,A_{1}=AI\cap BC$  and  $B_{1}=BI\cap AC.$  Let  $l_{a}$  be the line through  $A_{1}$  which is parallel to  $AC$  and  $l_{b}$  be the line through  $B_{1}$  parallel to  $BC.$  Let  $l_{a}\cap CI=A_{2}$  and  $l_{b}\cap CI=B_{2}.$  Also  $N=AA_{2}\cap BB_{2}$  and  $M$  is the midpoint of  $AB.$  If  $CN\parallel IM$  find  $\frac{CN}{IM}$ .

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