
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
Jia draws five lines in a plane such that no three lines are concurrent. If any two lines determine a unique intersection point, Jia can get one candy. Additionally, if there is a set of parallel lines, Jia can also get one candy. For example, in a particular configuration with seven intersection points and one set of parallel lines, Jia can get 8 candies. What are the possible numbers of candies Jia can obtain?

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