
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
Consider the graphs of 
\[(1)\qquad y=x^2-x+3\]
and
\[(2)\qquad y=x^2+x+5\]
on the same axis.
Both parabolas share the same general shape. Determine which statement is correct:
- A) the graphs of both functions coincide.
- B) the graph of (1) is below the graph of (2).
- C) the graph of (1) is to the right of the graph of (2).
- D) the graph of (1) is to the left of the graph of (2).
- E) the graph of (1) is above the graph of (2).
- **A)** the graphs of both functions coincide.
- **B)** the graph of (1) is below the graph of (2).
- **C)** the graph of (1) is to the right of the graph of (2).
- **D)** the graph of (1) is to the left of the graph of (2).
- **E)** the graph of (1) is above the graph of (2).

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