
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
For real numbers $x, y$, a new operation $x \ast y$ is defined as $x \ast y = ax + by + 2010$, where $a, b$ are constants, and the equation's right side involves the usual addition and multiplication operations. Given that $3 \ast 5 = 2011$ and $4 \ast 9 = 2009$, find the value of $1 \ast 2$.

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