
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
The sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ is $S_n$, and it is given that $S_3 = 6$, $a_1 = 4$. If vector $\overrightarrow{m} = (a_5, 3)$ and vector $\overrightarrow{n} = (1, a_3)$, calculate the projection of vector $\overrightarrow{m}$ onto the direction of vector $\overrightarrow{n}$.

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