
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
Line $l$ passes through the point $(0,4)$ and is perpendicular to the $y$-axis. If the graph of the quadratic function $y=(x-a)^{2}+(x-2a)^{2}+(x-3a)^{2}-2a^{2}+a$ has two distinct intersection points with line $l$, and its axis of symmetry is to the right of the $y$-axis, determine the range of values for $a$.

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