
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
Based on the conversation between $x$ and $y$ below, answer the following questions:<br/>$x$: Both $y$ and I are polygons, and the sum of our interior angles is $1440^{\circ}$;<br/>$y$: The ratio of the number of sides of $x$ to the number of sides of me is $1:3$.<br/>$(1)$ Find the sum of the exterior angles of $x$ and $y?<br/>$(2)$ Find the number of sides of $x$ and $y respectively?<br/>$(3)$ Determine how many diagonals $y$ has in total?

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