Solving system of 4 non-linear inequalities

Hello out there! Your help is needed. I am trying to solve this system of non-linear inequalities using solve

syms x y
cond1 = ( 5^(1-x)) + (exp(-(-log(0.3))^(y))) * ((20^(1-x))-( 5^(1-x))) > (2.5^(1-x)) + (exp(-(-log(0.1))^(y))) * ((62.5^(1-x))-(2.5^(1-x)));
cond2 = ( 5^(1-x)) + (exp(-(-log(0.3))^(y))) * ((20^(1-x))-( 5^(1-x))) < (2.5^(1-x)) + (exp(-(-log(0.1))^(y))) * ((  75^(1-x))-(2.5^(1-x)));

cond3 = (15^(1-x)) + (exp(-(-log(0.9))^(y))) * ((20^(1-x))-(15^(1-x))) > (2.5^(1-x)) + (exp(-(-log(0.7))^(y))) * ((32.5^(1-x))-(2.5^(1-x)));
cond4 = (15^(1-x)) + (exp(-(-log(0.9))^(y))) * ((20^(1-x))-(15^(1-x))) < (2.5^(1-x)) + (exp(-(-log(0.7))^(y))) * ((  34^(1-x))-(2.5^(1-x)));

conds = [cond1 cond2 cond3 cond4];

sol = solve(conds, [x y], 'ReturnConditions', true);

sol.x
sol.y
sol.parameters
sol.conditions

But I am getting this message as a result:

Warning: Unable to find explicit solution. For options, see help. 
> In solve (line 317) 
ans = 
Empty sym: 0-by-1
ans =
Empty sym: 0-by-1
ans =
Empty sym: 1-by-0
ans =
Empty sym: 0-by-1
>> 

Am I doing something wrong or is it just that Matlab solve cannot handle this type of problems? If the latter, can you please direct me to the proper tool I should use?

The correct answer for this problem is 0.26 < x < 0.35 and 0.66 < y < 0.74.

Any help is very much appreciated it!!