
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 $ABC$, $\angle C = \theta$ and $\angle B = 2\theta$, where $0^{\circ} < \theta < 60^{\circ}$. A circle with center $A$ and radius $AB$ intersects $AC$ at $D$ and intersects (or if necessary, extended $BC$) at $B$ and $E$ (where $E$ can coincide with $B$). Determine the condition for $EC = AD$ to hold.

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