
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 equation of the curve C as $$\begin{cases} x=1+2t \\ y=at^{2}\end{cases}$$ (where t is the parameter, $a\in \mathbb{R}$), and the point M(5,4) lies on the curve C.  
(1) Find the value of the constant $a$;  
(2) Find the standard equation of the curve C.

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