
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 diagram, \(ABCD\) is a square. Point \(F\) is on \(AB\) with \(BF = 2 \cdot AF\). Point \(E\) is on \(AD\) with \(\angle FEC = \angle BCE\). If \(0^{\circ} < \angle ECD < 45^{\circ}\), what is the value of \(\tan (\angle ECD)\)?

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