
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
A small insect falls on a point $P_{0}$ on the number line. It jumps left one unit to $P_{1}$ for the first time, right two units to $P_{2}$ for the second time, left three units to $P_{3}$ for the third time, and right four units to $P_{4}$ for the fourth time. After jumping according to the above pattern for $100$ times, it lands on a point $P_{100}$ on the number line representing the number $2019$. Find the initial position $P_{0}$ of this insect, which corresponds to the number ______.

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