
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 sequence $\{a_n\}$, it satisfies: $a_{n+1}= \begin{cases} \frac{a_n}{2}, & a_n \text{ is even} \\ 3a_n+1, & a_n \text{ is odd} \end{cases}$, if $a_1=5$, calculate the value of $a_1+a_2+a_3$.

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