
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
Given a binary operation $\star$ on ordered pairs of integers defined as $(a, b) \star (c, d) = (a - 2c, b + 2d)$, if $(2, -4) \star (1, -3)$ and $(x, y) \star (2, 1)$ represent identical pairs, determine the value of $x$.

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