
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 line $l$ as $\begin{cases} x=2+ \frac {1}{2}t \\ y= \frac { \sqrt {3}}{2}t \end{cases}$ (where $t$ is the parameter), and the polar equation of curve $C$ as $\rho^{2}\cos 2\theta=1$.

$(1)$ Find the standard equation of curve $C$;  
$(2)$ Find the length of the chord cut from curve $C$ by line $l$.

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