
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
Find all values of \( a \), for each of which, for any \( x \), the smallest of the two numbers

\[ 2^{x-1} - 3^{4-x} + a \quad \text{and} \quad a + 5 - x^{3} - 2x \]

is negative.

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