
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
The graph of $y=ax^2+bx+c$ is given, where $a$, $b$, and $c$ are integers. Find $a$.
In the coordinate system, the vertex of the parabola is located at $(2, 5)$, and another point on the graph is $(1, 2)$.

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