
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
Consider the sequence $b_1, b_2, b_3, \dots$ defined by $b_1 = 2$, $b_2 = 3$, and for $k \geq 3$,
\[b_k = \frac{1}{2} b_{k-1} + \frac{1}{3} b_{k-2}.\]
Find the sum $T = b_1 + b_2 + b_3 + \dots.$

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