
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
Find the Jordan normal form of the operator  $e^{d/dt}$  in the space of quasi-polynomials  $\{e^{\lambda t}p(t)\}$  where the degree of the polynomial  $p$  is less than  $5$ , and of the operator  $\text{ad}_A$ ,  $B\mapsto [A, B]$ , in the space of  $n\times n$  matrices  $B$ , where  $A$  is a diagonal matrix.

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