
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 pair of concentric circles, chords   $AB,BC,CD,\dots$  of the outer circle are drawn such that they all touch the inner circle. If  $\angle ABC = 75^{\circ}$ , how many chords can be drawn before returning to the starting point ?
![Image](https://i.imgur.com/Cg37vwa.png)

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