
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
Let \( f(x) \) be an odd function with domain \( \mathbb{R} \) and a period of 5. If \( f(1) < -1 \) and \( f(4) = \log_{2}{a} \), then the range of the real number \( a \) is __________.

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