
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
In a Cartesian coordinate system, a moving object passes through point A (0, 9). The equation of its trajectory is $y = ax^2 + c$ (where $a < 0$). Let D = (6, 7) be a given interval on the x-axis.
1. To ensure that the object falls within interval D, determine the range of values for $a$.
2. If the object also passes through point P (2, 8.1) during its motion, can it fall within interval D? Provide an explanation.

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