
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 that $\overrightarrow{c}$ and $\overrightarrow{d}$ are unit vectors with an angle of $60^{\circ}$ between them, and $\overrightarrow{a}= \overrightarrow{c}+3 \overrightarrow{d}$, $\overrightarrow{b}=2 \overrightarrow{c}$, then the projection of $\overrightarrow{b}$ in the direction of $\overrightarrow{a}$ is \_\_\_\_\_\_.

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