
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
Recite the following definitions:  
(1) Definition of mapping: A and B are two sets. If according to some correspondence rule $f$, for every element $x$ in set A, there is a unique element $y$ in set B corresponding to it, then such a correspondence is called a mapping from set A to set B. It is denoted as ______.  
(2) Prism: There are two faces that are ______ to each other, the rest of the faces are quadrilaterals, and the common edge of every two adjacent quadrilaterals is ______.  
(3) Right prism: A right prism is a prism whose lateral edges are ______ to the base, and the base is a ______ polygon.  
(4) Existence of Zero Theorem: Suppose the function $f(x)$ is continuous on the closed interval $[a, b]$, and ______, then there is at least one zero of the function $f(x)$ in the open interval $(a, b)$, that is, there is at least one point $x$ ($a < x < b$) such that $f(x) = 0$.  
(5) Solid Geometry Axiom Three: If two non-coincident planes have ______, then they have exactly one ______.

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