
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
Determine $a + n$ if
\[
\left(\begin{pmatrix} 1 & 3 & a \\ 0 & 1 & 5 \\ 0 & 0 & 1 \end{pmatrix}^n\right)^2 = \begin{pmatrix} 1 & 54 & 8008 \\ 0 & 1 & 90 \\ 0 & 0 & 1 \end{pmatrix}.
\]

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