
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 in $\triangle ABC$, $D$ is a point on side $AB$, $\overrightarrow{CD} =\lambda \left( \frac{ \overrightarrow{CA}}{|\overrightarrow{CA}|} + \frac{ \overrightarrow{CB}}{|\overrightarrow{CB}|} \right)$, $|\overrightarrow{CA}|=2$, $|\overrightarrow{CB}|=1$, if $\overrightarrow{CA}=b$, $\overrightarrow{CB}=a$, express $\overrightarrow{CD}$ in terms of $a$, $b$.

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