
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
In $\triangle ABC$, $D$ is the midpoint of side $AB$, let $\overrightarrow{BC} = \overrightarrow{a}$, $\overrightarrow{BA} = \overrightarrow{c}$. Express the vector $\overrightarrow{CD}$ in terms of $\overrightarrow{a}$ and $\overrightarrow{c}$.

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