
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
 $A=\{1,2,3,4,5,6,7,8\} .$  How many functions  $f: A \rightarrow A$  are there such that  $f(1)<f(2)<f(3)$ [list=1]
[*]  ${{8}\choose{3}}$ [*]  ${{8}\choose{3}}5^{8}$ [*]  ${{8}\choose{3}} 8^{5}$ [*]  $\frac{8 !}{3 !} $ [/list]

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