
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 inequality $\frac{1}{a} + \frac{9}{b} = 1$ holds true for the positive numbers $a$ and $b$. Find the range of values for the real number $m$ such that the inequality $a + b \geq -x^2 + 4x + 18 - m$ holds true for any real number $x$.

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