
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
Let the function $f(x) = 3^{|x-1|} - 2x + a$, and $g(x) = 2 - x^2$. Determine the range of the real number $a$ such that on the interval $(0, 3)$, the graph of $f(x)$ is above the graph of $g(x)$.

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