
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 depicted, where \(a\), \(b\), and \(c\) are known to be integers. Find the value of \(a\) for this newly formed parabola.

Given that the vertex of the parabola is at \(x=2\) where \(y=5\), and one other point on the graph is \((1, 2)\).

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