
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
$R_{1}$ and $R_{2}$ are regular polygons. $R_{2}$ has $p$ more sides than $R_{1}$; the central angle corresponding to one side in $R_{1}$ is $\gamma$ greater than in $R_{2}$. How many sides do $R_{1}$ and $R_{2}$ have? Numerical example: $p=5, \gamma=12^{\circ} / 7$ - If only $p$ is given, what are the possible values for $\gamma$? For example, $p=2$ - Given $\gamma$, how can you determine the possible values for $p$? For example, $\gamma=30^{\circ}$; $12^{\circ}$.

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