
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 
\[(1)\qquad y = x^3 - x^2 - \frac{1}{2}x + 2\]
and
\[(2)\qquad y = x^2 + \frac{3}{2}x + 4\]
on the same set of axes. Determine the relative position of the graphs at their point of intersection, assuming \((2)\) intersects \((1)\) from below upwards.
A) \((2)\) passes from above downwards through \((1)\) on the left side.
B) \((2)\) passes from below upwards through \((1)\) on the left side.
C) \((2)\) only touches \((1)\) but does not cross.
D) \((2)\) crosses \((1)\) twice, entering from above.

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