
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
The equation of the parabola obtained by shifting the parabola $y=2x^{2}$ $4$ units to the left and then $1$ unit up is given by the expression $y=2(x-h)^{2}+k$, where $h$ and $k$ are constants. Determine the values of $h$ and $k$.

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