
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
Given the matrix equation
\[
\begin{pmatrix} 1 & 3 & b \\ 0 & 1 & 5 \\ 0 & 0 & 1 \end{pmatrix}^m = \begin{pmatrix} 1 & 27 & 3005 \\ 0 & 1 & 45 \\ 0 & 0 & 1 \end{pmatrix},
\]
find the value of $b + m$.

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