
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
A piece of paper is folded in half. A second fold is made such that the angle marked below has measure \(\phi\) \((0^{\circ}<\phi<90^{\circ})\), and a cut is made as shown below.

When the piece of paper is unfolded, the resulting hole is a polygon. Let \(O\) be one of its vertices. Suppose that all the other vertices of the hole lie on a circle centered at \(O\), and also that \(\angle XOY=144^{\circ}\), where \(X\) and \(Y\) are the vertices of the hole adjacent to \(O\). Find the value(s) of \(\phi\) (in degrees).

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