
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 positive integer  $n>1$  is called beautiful if  $n$  can be written in one and only one way as  $n=a_1+a_2+\cdots+a_k=a_1 \cdot a_2 \cdots a_k$  for some positive integers  $a_1, a_2, \ldots, a_k$ , where  $k>1$  and  $a_1 \geq a_2 \geq \cdots \geq a_k$ . (For example 6 is beautiful since  $6=3 \cdot 2 \cdot 1=3+2+1$ , and this is unique. But 8 is not beautiful since  $8=4+2+1+1=4 \cdot 2 \cdot 1 \cdot 1$  as well as  $8=2+2+2+1+1=2 \cdot 2 \cdot 2 \cdot 1 \cdot 1$ , so uniqueness is lost.) Find the largest beautiful number less than 100.

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