
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
If for the function f(x) = x - $\sqrt{x^2 + x}$ and g(x) = log$_{27}$x - log$_{9}$x + a*log$_{3}$x, and for all x$_1$ in the interval (1, +∞), there exists x$_2$ in the interval [3, 9] such that f(x$_1$) > g(x$_2$), determine the range of values for 'a'.

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