
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
Square $XYZW$ has side length $2$ units. Points $P$ and $Q$ are on sides $XZ$ and $ZW$, respectively, with $XP = WQ$. When the square is folded along the lines $YP$ and $YQ$, sides $XY$ and $WY$ coincide and lie on diagonal $ZW$. The length of segment $XP$ can be expressed in the form $\sqrt{t} - n$ units. Find the integer value of $t+n$.

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