
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 a circular sector AOB where angle AOB is $60^{\circ}$. The lengths of the radii OA and OB are increased by $5\%$, turning them into segments OA$_{1}$ and OB$_{1}$. Which is longer: the length of the segment A$_{1}$B$_{1}$ or the length of the arc AB? Justify your answer. (The circumference of a circle with radius $R$ is $2 \pi R$.)

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