
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
Let  $ A_i,i=1,2,\dots,t$  be distinct subsets of the base set  $\{1,2,\dots,n\}$  complying to the following condition  $$  \displaystyle A_ {i} \cap A_ {k} \subseteq A_ {j} $$  for any  $1 \leq i <j <k \leq t.$  Find the maximum value of  $t.$ Thanks @dgrozev

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