
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 the acute triangle \( \triangle ABC \), \( \angle CAB = 60^\circ \), \( BC = 2 \), and \( D \) is a point on the external angle bisector of \( \angle BAC \). Given that \( \overrightarrow{CD} = \overrightarrow{CA} + \lambda\left(\frac{\overrightarrow{AC}}{|\overrightarrow{AC}|} + \frac{\overrightarrow{AB}}{|\overrightarrow{AB}|}\right) \), determine the range of the real number \( \lambda \).

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