
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
If the chord length intercepted by the curve $ \begin{cases} x=1+4\cos \theta \\ y=3+4\sin \theta \end{cases} (\theta \text{ is the parameter}) $ on the line $x-y+t=0$ is $4 \sqrt {2}$, then the value of the real number $t$ is _______.

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