
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
Martha has a lot of pins in her sewing box. The first time she took out two pins, and each subsequent time she took out $k$ pins more than the previous time. It turned out that the tenth time she took out more than 45 pins, and the fifteenth time she took out less than 90 pins. Write down all possible values of $k$.

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