
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 $PQRS$ has side length $\sqrt{2}$ units. Points $T$ and $U$ are on sides $PQ$ and $RQ$, respectively, with $PT = QU$. When the square is folded along the lines $ST$ and $SU$, sides $PS$ and $RS$ coincide and lie on diagonal $QS$. The length of segment $PT$ can be expressed in the form $\sqrt{a} - b$ units. What is the integer value of $a + b$?

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