
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
For any function $f(x)$ defined on $\mathbb{R}$, if a real number $x$ satisfies $f(x) = x$, then $x$ is called a fixed point of the function $f(x)$. If the function $f(x) = ax^2 + (2a-3)x + 1$ has exactly one fixed point, then the set of values for the real number $a$ is.

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