
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 branches of the graph of a quadratic trinomial are directed upwards, its vertex is at the point \((1/4, -9/8)\), and the point on this graph with an abscissa of 1 has an integer ordinate. Find the smallest possible value of the leading coefficient and report it as a decimal to two decimal places (e.g., 3.14).

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