
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
1. (Optional question on coordinate systems and parametric equations) If the polar equation of a curve is $p=2\sin\theta+4\cos\theta$, and a Cartesian coordinate system is established with the pole as the origin and the polar axis as the positive x-axis, then the Cartesian equation of the curve is.
2. (Optional question on inequalities) For real numbers $x, y$, if $|x-1|\leq1$ and $|y-2|\leq1$, then the maximum value of $|x-2y+1|$ is.

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