
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 the rectangle below, line segment $PQ$ separates the rectangle into 2 sections. What is the largest number of sections into which the rectangle can be separated when $5$ line segments (including $PQ$) are drawn through the rectangle? [asy]
size(3cm,3cm);
pair A,B,C,D,P,Q;
A=(0,0);
B=(1.5,0);
C=(1.5,1);
D=(0,1);
draw (A--B--C--D--A);
P=(0.8,0);
Q=(1.2,1);
draw(P--Q);
label("P",P,S);
label("Q",Q,NNE);
[/asy]

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