
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
In a coordinate plane, there are 20 lattice points arranged in a rectangle of 5 rows and 4 columns, each one unit apart. Segment $PQ$ meets segment $RS$ at point $T$. Given the coordinates $P(0,4)$, $Q(4,0)$, $R(1,0)$, and $S(3,3)$, find the length of segment $PT$.

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