
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
Given a function $f(x)$ with domain $\mathbb{R}$ that satisfies $f(2-x)=f(x)$, and for $x \geqslant 1$, $f(x) = 2^x + \sqrt{x^2 - x + 2}$. If $f(\log_a(2a)) < 6$ ($a > 0$ and $a \ne 1$), determine the range of the real number $a$.

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