
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 rule is given according to which each pair of integers \( X \) and \( Y \) is assigned a number \( X \nabla Y \). (The symbol \(\nabla\) denotes the application of the rule to the numbers \( X \) and \( Y \).) It is known that for any integers \( X \) and \( Y \), the following properties hold:

1) \( X \nabla 0 = X \)
2) \( X \nabla (Y - 1) = (X \nabla Y) - 2 \)
3) \( X \nabla (Y + 1) = (X \nabla Y) + 2 \).

Find the formula that describes the action of the given rule and solve the equation

\[ X \nabla X = -2019 \]

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