
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 right triangle  $ ABC$ ,  $ BC \equal{} 5$ ,  $ AC \equal{} 12$ , and  $ AM \equal{} x$ ;  $ \overline{MN} \perp \overline{AC}$ ,  $ \overline{NP} \perp \overline{BC}$ ;  $ N$  is on  $ AB$ . If  $ y \equal{} MN \plus{} NP$ , one-half the perimeter of rectangle  $ MCPN$ , find the value of $y$.

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