
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 the largest integer \( a \) such that the expression

\[ 
a^2 - 15a - (\tan x - 1)(\tan x + 2)(\tan x + 5)(\tan x + 8) 
\]

is less than 35 for all values of \( x \in (-\pi/2, \pi/2) \). 



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