
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 the parametric equations of curve $C$ are
$$
\begin{cases}
x=3t, \\
y=2t^{2}+1
\end{cases}
(t \text{ is the parameter}).
$$

(1) Determine the positional relationship between points $M_1(0,1)$, $M_2(5,4)$ and curve $C$;

(2) Given that point $M_3(6,a)$ is on curve $C$, find the value of $a$.

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