
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
Please add 4 scales on a scaleless ruler with a length of 13 cm, so that any integer centimeter length between 1 and 13 can be measured (Note: measurement refers to being able to measure directly, for example, 5 can be directly measured by the scale of 5 or indirectly by the difference between the scales of 6 and 11, but not by adding 2 and 3. Additionally, 0 and 13 are the original scales and do not need to be added). For instance, 1, 2, 6, 10 is a set of scales that meets the requirements. Please find another set of scales that meets the requirements.

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