
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
Given two paper strips, one longer at $23 \mathrm{~cm}$ and one shorter at $15 \mathrm{~cm}$, and segments of the same length $x$ are cut off from both strips, find the minimum length of the segment $x$ such that the remaining length of the longer strip is at least twice the length of the remaining shorter strip.

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