
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
Definition: The ratio $k$ of the length of the base of an isosceles triangle to the length of the height on the base is called the "characteristic value" of this isosceles triangle. If the perimeter of isosceles $\triangle ABC$ is $100$ cm and $AB=18$ cm, then the "characteristic value" $k$ of this triangle is $\_\_\_\_\_\_$.

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