
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
In the small squares of "$\square 1\square 2\square 3\square 4\square 5\square 6\square 7\square 8\square 9$", fill in the symbols "$+$" or "$-$". If it is possible to make the algebraic sum equal to $m$, then the number $m$ is called an "expressible number". For example, $1$ is an "expressible number" because $+1+2-3-4+5+6-7-8+9$ is one way to express $1$.  
$(1)13 $______ is an "expressible number", 14 $______ is an "expressible number" (fill in "is" or "is not");  
$(2)$ There are ______ "expressible numbers" in total;  
$(3)$ Find out how many different ways can $27$ be expressed.

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