
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
A quadratic function is given by $y=ax^2-12ax+36a-5$. Its graph lies below the x-axis in the interval $4<x<5$ and above the x-axis in the interval $8<x<9$. Determine the value of the coefficient $a$.

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